Over the course of time, most AMD cards have gained 10 - 30% performance over their launch numbers in DX 11, while NVIDIA cards have not. It would seem, NVIDIA doesn't optimize drivers for a 1 generations old card anymore.
Some benchmark suite averages such as Tom's paint the GTX 1060 with a > 20% performance advantage over the RX 480, while some benchmark suite averages paint the 1060 with 5% above - 5% performance loss in comparison. It all depends on the games being run on the cards, and the settings used during those runs.
Under Vulkan and DX 12, which new games are now shipping with, AMD cards easily surpass the NVIDIA rivals, except in the case of the 1070 and 1080, simply due to NVIDIA's brute force approach.
When you also take into consideration the lost upgrade path of multi-GPU support with the 1060, and that G-Sync would cost another premium to buy into VS Free sync, which doesn't necessarily drive the cost of the screen up, the NVIDIA offering is even less competitively priced.